Centrally essential group algebras and classical rings of fractions
type: Item
instance of: scholarly article
title: Centrally essential group algebras and classical rings of fractions
zbMATH Open document ID: 1489.16021
DOI: 10.1134/S1995080221120246
published in: Lobachevskii Journal of Mathematics
publication date: 2021-12-22T00:00:00Z
review text: A ring \(R\) with center \(C(R)\) is said to be centrally essential if the module \(R_{C(R)}\) is an essential extension of the module \(C(R)_{C(R)}\). In this case, for every non-zero element \(a\) of \(R\) there exist two non-zero central elements \(x, y\) with \(ax = y\). The main result of the paper is Theorem 1: Any centrally essential group algebra over any field has the two-sided classical ring of fractions. In addition, the group algebra over a field is centrally essential if and only if it has the classical right ring of fractions which is a centrally essential ring.
reviewed by: A. V. Tushev
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16S85
Mathematics Subject Classification ID: 20C07
zbMATH DE Number: 7450552
zbMATH Keywords: group algebra
zbMATH Keywords: classical ring of fractions
zbMATH Keywords: centrally essential ring
author: Oleg V. Lyubimtsev
author: A. A. Tuganbaev
MaRDI profile type: Publication
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full work available at URL: s1995080221120246
OpenAlex ID: W4200231697
description: scientific article; zbMATH DE number 7450552